Domain and Range of Functions

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input from its domain.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

How can you determine if a relation is a function?

Back

A relation is a function if every input has exactly one output. This can be tested using the vertical line test on a graph.

Front

What is the vertical line test?

Back

The vertical line test states that if a vertical line intersects a graph at more than one point, then the relation is not a function.

Front

Given the function f(x) = x + 4, what is the range if the domain is {1, 7, 10}?

Back

The range is {5, 11, 14}.

Front

Identify the range of the function y = 4x - 12 for the domain {2, 3, 10}.

Back

The range is {-4, 0, 28}.

Front

What is an appropriate domain for the function f(x) = 15x + 20 if x represents hours worked?

Back

An appropriate domain is any value between 0 and 5.

Front

What does it mean for a function to be defined?

Back

A function is defined when there is a corresponding output for every input in its domain.

Front

What is a one-to-one function?

Back

A one-to-one function is a function where each output is produced by exactly one input.